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  • The 2-rainbow domination numbers of ▫$\boldsymbol{C}_4 \Box \boldsymbol{C}_n$ and $\boldsymbol{C}_8 \Box \boldsymbol{C}_n$▫
    Shao, Zehui ...
    A ▫$k$▫-rainbow dominating function (kRDF) of ▫$G$▫ is a function ▫$f:V(G)\rightarrow {\mathcal {P}}(\{1,2,\ldots ,k\})$▫ for which ▫$f(v)=\emptyset$▫ we have ▫$\bigcup \nolimits _{u\in ... N(v)}f(u)=\{1,2,\ldots ,k\}$▫. The weight ▫$w(f)$▫ of a function ▫$f$▫ is defined as ▫$w(f)=\sum _{v\in V(G)}\left| f(v)\right|$▫. The minimum weight of a kRDF of ▫$G$▫ is called the ▫$k$▫-rainbow domination number of ▫$G$▫, which is denoted by ▫$\gamma _{rk}(G)$▫. In this paper, we determine the exact values of the 2-rainbow domination numbers of ▫$C_4\Box C_n$▫ and ▫$C_8\Box C_n$▫. It follows that ▫$\gamma _{r2} \ne 2\gamma$▫ for graphs ▫$C_4\Box C_n$▫ ▫$(n \ge 4)$▫ and ▫$C_8\Box C_n$▫ ▫$(n \ge 8)$▫, answering in part a question raised by Brešar.
    Vir: National Academy Science Letters. - ISSN 0250-541X (Vol. 42, iss. 5, 2019, str. 411-418)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2019
    Jezik - angleški
    COBISS.SI-ID - 16771355

    Povezava(-e):

    https://link.springer.com/article/10.1007%2Fs40009-018-0779-y
    DOI

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